Lesson 2

• Groups of 2
• Display the expression.
• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”

• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.
• Monitor for students who estimate by using \(10,\!000 \times 900\).

• Invite students to share estimates.
• “¿Por qué \(10,\!000 \times 900\) es una buena estimación del producto?” // “Why is \(10,\!000 \times 900\) a good estimate for the product?” (10,000 is just 1 more than 9,999 and 896 is close to 900.)
• “¿Cuál es el valor de \(10,\!000 \times 900\)? ¿Cómo lo saben?” // “What is the value of \(10,\!000 \times 900\)? How do you know?” (9,000,000 because the two numbers have 6 factors of 10 combined.)

• revise their answer after examining Kiran’s mistake.
• recognize that \(650 \times 10 = 6,\!500\) so \(650 \times 27\) has to be much greater than 5,850.
• can explain why Kiran should be multiplying \(650 \times 2 \times 10\).
• recognize that \(20 \times 50 = 1,\!000\) so there should be three zeros in the second partial product.

When students determine Kiran's error and make sense of his work, they interpret and critique the work of others (MP3).

• Display or write for all to see.

  \(650 \times 27\)

• Display each number in a different corner of the room:
  14,000
  18,000
  13,000
  19,000

• “Cuando yo diga ‘ya’, párense en la esquina que tenga el número que crean que es la estimación más razonable de \(650 \times 27\). Prepárense para explicar cómo razonaron” // “When I say go, stand in the corner with the number that you think is the most reasonable estimate for \(650 \times 27\). Be prepared to explain your reasoning.”
• 1 minute: quiet think time
• Ask a representative from each corner to explain their reasoning.
• “¿Alguien quiere cambiar de esquina?” // “Does anyone want to switch corners?”
• Ask a student who switched corners to explain their reasoning.
• “Ahora van a encontrar este producto y a analizar un trabajo” // “Now you are going to find this product and analyze some work.”

• Groups of 2
• 5–7 minutes: partner work time

• Ask previously identified students to share their thinking.
• Display Kiran's work.
• “¿Por qué 5,850 no tiene sentido?” // “Why doesn’t 5,850 make sense?” (\(650 \times 10 = 6,\!500 \) so \(650 \times 27\) should be a lot larger than 6,500.)
• “¿Qué tiene sentido en el trabajo de Kiran?” // “What makes sense about Kiran’s work?” (\(650 \times 2 =1,\!300\), but he needs to multiply \(650\times2\times10\).)
• Display a student's solution or the image from the student solution.
• “¿Cómo sabemos que 17,550 es una estimación razonable del producto?” // “How do we know that 17,550 is a reasonable value for the product?” (Because \(600 \times 30 =18,\!000\).)

The purpose of this activity is for students to practice multiplying multi-digit numbers that have one or more digits of 0 at the end. Monitor for students who:

• use the standard algorithm to evaluate \(6,\!700 \times 89\).
• multiply the product \(67 \times 89\) by 10 to find the value of the product \(670 \times 89\).
• multiply the product of \(670 \times 89\) by 10 to find the value of the product \(6,\!700 \times 89\).

Students who observe that \(670 = 10 \times 67\) and \(6,\!700 = 10 \times 670\) and use these relationships to find the values of the products are observing regularity in repeated reasoning and using their knowledge of how to multiply a whole number by 10 (MP7, MP8).

• Groups of 2

• 5–7 minutes: independent work time
• 5–7 minutes: partner discussion

• Display the product \(6,\!700 \times 89\):
• Ask previously identified students to share their solutions.
• Display student work or the image from the sample response:

  

  

• “¿Qué relación hay entre \(670\times89\) y \(6,\!700\times89\)?” // “What is the relationship between \(670\times89\) and \(6,\!700\times89\)?” (The product \(6,\!700\times89\) is ten times larger because one of the factors is ten times greater.)
• “¿Qué relación hay entre \(67 \times 89\) y \(6,\!700 \times 89\)?” // “What is the relationship between \(67 \times 89\) and \(6,\!700 \times 89\)?” (The product \(6,\!700 \times 89\) is 100 times as large as \(67 \times 89\) since 6,700 is \(100 \times 67\).)